1. Tier 2 Interventions for Mathematics Denver Public Schools August 2009 1

2. Overview of Morning Process for identifying recommended interventions Supporting DPS Core Mathematics with Tier 2 Interventions Preview DPS recommended interventions  Math Navigator: grades 2-10  ALEKS: grades 3-12  ORIGOmath: grades 1-2  Aim for Algebra (pilot): grades 8-9 2

3. Screen of Intervention Programs Clear directions for guided and independent practice Instructional materials with adequate practice (concepts & procedures) and sufficient review (distributed, cumulative, & varied) Additional support for ELLs Identification of common misconceptions with suggestions to address them Mathematically correct content Multiple assessments (diagnostic, progress monitoring, summative) with clear guidelines for use and instructional interpretation

4. Research-Based Recommendations for Mathematics Interventions Screen all students to identify those at risk Focus intensely on in-depth treatment of whole numbers in K- 5 and on rational numbers in 4-8 Provide explicit and systematic instruction (models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, & frequent cumulative review) Include instruction on solving word problems Include opportunities for students to work with visual representations of mathematical ideas Devote about 10 minutes per session to building fluent retrieval of basic arithmetic facts 4

5. Assisting Students Struggling with Mathematics: Response to Instruction Begin with high-quality instruction and universal screening for all students Core program (Everyday Mathematics, Connected Mathematics, or Discovering Mathematics) Instructional time as described in Best Practice documents Differentiated instruction within core program to support students Periodic assessment using tools within core program 5

6. Universal Screening in Mathematics 6

7. Universal Screening: Grade 3 Current third graders  Spring 2009 DPS benchmark results  Standards-based progress reports with a focus on Number Sense and Computation  Diagnostic screener 7

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9. Implementing Tier 2 Interventions Select an intervention program Identify students to be served, create an order and send order (electronically) to Maggie Wolfe in ERS Create an intervention schedule Teachers delivering intervention attend central professional development 9

10. Program Preview Mathematics Navigator from America’s Choice ORIGOmath from ORIGOeducation ALEKS—an online system 10

11. Mathematics Navigator

12. 12 Introduction to Mathematics Navigator Does not repeat initial teaching Focuses on revising misconceptions Encourages students to approach the mathematics from several angles Provides learning opportunities beyond solving problems—analyze work for errors, test validity of their work against others’ work, try multiple strategies to determine if prior knowledge holds true, and modify or invent similar problems

13. 13 Mathematics Navigator Program Design Targeted Concepts Algebraic Structure of Arithmetic Prior Knowledge and Misconceptions Language-Rich Environment Better Learners of Mathematics Instructional Support

14. Module Design 20 days for each module  Module design in elementary units includes two check-points  Module design in secondary units includes a check-point every 5 days Recommended instructional time: 35-45 minutes a minimum of 3 days a week in addition to core instruction Group size  Elementary: up to 10 students  Secondary: up to 30 students 14

15. 15 Instructional Support Overview Instructional guidance ELL Support Formal and Informal Assessments  Diagnostic screeners  Pre- and post-tests  Checkpoints

16. Universal Screening: Grades 4-10 16

17. Universal Screening: Grade 3 Current third graders  Spring 2009 DPS benchmark results  Standards-based progress reports with a focus on Number Sense and Computation  Diagnostic screener 17

18. 18 Getting Started with Year Administer Screener Analyze assessment data and determine modules to implement and place order

19. 19 Getting Started with a Module Day 1 Administer and Score Pre-Test Record Pre-Test data on the Pre-Test/Post- Test Profile Consider Pre-Test results for individual student and for class

20. 20 Getting Started with a Session Skill Cards (using quick response boards) Skill Practice (in student book) Solo Work: Problem 1 Partner Work: Problem 1 Probing for Understanding Solo Work: Problem 2 Partner Work: Problem 2 Probing for Understanding Closing the Lesson

21. 21 Instructional Support within Modules Instructor Edition  Purpose of Module  Goals for the Module  Day-by-Day Overview  English Language Learner Considerations  Types of Assessment & Record Keeping Chart of Rituals Study Cards Materials List Checkpoints Checkpoint Profile Class Profile

22. Mathematics Navigator in DPS 22

23. ALEKS 23

24. What is ALEKS? Assessment and LEarning in Knowledge Spaces Only online intervention recommended by DPS for mathematics intervention 24

25. Features of ALEKS Assessment and learning with Standards- Based Content for Grades 3-12 Monitors Student, Class, School and District Progress Toward State Standards Fully Bilingual – English and Spanish for Grades 3-9 Unlimited Online Access – PC & Mac Compatible 25

26. How Does ALEKS Work? Initial assessment determines students’ topic mastery Multi-colored chart generated for each student Student works in learning mode to master new topics Continual assessment aids students’ retention of new learning 26

27. ALEKS in Action http://www.aleks.com/video/quick_tour 27

28. ALEKS Course Products Mathematics-LV 3 (with Quick Tables) for Tier 2 Grades 3-4 Mathematics-LV 4 (with Quick Tables) for Tier 2 Grade 5 Mathematics-LV 5 (with Quick Tables) for Tier 2 Grade 6 Essential Mathematics (with Quick Tables) for Tier 2 Grades 8, 9, 10 High School Preparation for Algebra 1 for Tier 2 Grades 10, 11, 12 28

29. Quick Tables Demonstration http://www.aleks.com/video/qt_quick_tour 29

30. Assessment within ALEKS Initial Assessment Automatic Assessments Comprehensive Assessments Quizzes 30

31. Instructional Time Recommend minimum of 2 ½ hours per week in addition to core instruction Group size limited only by computer availability and teacher supervision 31

32. Sample Student Report 32

33. Sample Student Pie Chart 33

34. Other Important Information ALEKS can be used with either Windows or Mac with modifications Pricing will be determined by number of DPS students registered Professional development will be offered beginning in September 34

35. ORIGOmath 35

36. Universal Screening for Primary Grades Current second graders  Standards-based progress reports with a focus on Number Sense and Computation  Diagnostic screener from ORIGOmath: pre-test Current first graders  Standards-based progress reports with a focus on Number Sense and Computation  Diagnostic screener from ORIGOmath: prerequisite check list 36

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38. ORIGOmath Encourages students to justify and share their thinking Provides real-life contexts to explore mathematical ideas Provides a carefully developed sequence of learning experiences Emphasizes students’ critical thinking and reasoning Provides opportunities for students to practice computation facts in addition to problem solving 38

39. Teacher Sourcebook and Student Journals 39

40. Scope and Sequence 40

41. EM-like Models 41

42. One Unit for Two Weeks Each unit has five sessions Combine with Fundamentals game practice Recommend a two-week interval per unit Includes pre- and post-assessment for Grade 2 Includes pre-requisite checklist for Grade 1 and post-assessment 42

43. Assessment Tools 43

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45. Thank you! We know your time is valuable—especially at the start of a school year. Hopefully, this was enlightening as to plans in DPS for the 2009-2010 school year to provide support for our teachers and students in accessing the critical skills in mathematics. For further information, please contact DPS Intervention Coordinator in Teaching and Learning, Mathematics/Science: Dr. Kris O’Clair. 45

46. AIM for Algebra 46

47. Aim for Algebra: An Algebra intervention/prep program Developed by West Ed  Conceptually based  Standards-aligned Identified specific areas that most often become barriers to learning algebra Provides learning experiences that reinforce, refresh, or reteach important concepts 47

48. Increases Achievement Focuses on traditional barriers to success in algebra Uses purposeful sequencing and scaffolding of ideas Uses multiple strategies to reduce student misconceptions Uses manipulatives for hands-on learning 48

49. Organization Stand-alone units  Signed Number Operations2 weeks  Variables and expressions3-4 weeks  Ratio and Proportion4 weeks  Patterns3-4 weeks  The Coordinate Plane2-3 weeks  Inequalities4-6 weeks Allows for flexible programming Can be taught in any order but entire module should be taught sequentially 49

50. Coming Soon Number Theory for Algebra Exponents Rational Numbers Proportional Reasoning Equations and Formulas Data and Probability 50

51. Materials Each unit includes: Facilitator guide  Each unit is focused on three concepts or big ideas Consumable student pages (packaged for groups of 10)  Pre- and post-tests included  Daily task sheets 51

52. Teacher’s Role For each task  Purpose: helps focus the task.  Launch: begins the discussion and connects to prior learning before giving students their printed materials for the lesson  Facilitate the task: introduces task to whole group. Allows individual think time. Bring s group back together to check for understanding. Allows students to continue working on tasks individually or in groups. Circulates among groups and asks questions to help students who need guidance.  Summary: ensures students connect the task back to the stated purpose. Reinforces ideas. 52

53. Students’ Role  Justify their solutions in the context of the tasks  Explain their thinking and reasoning to others  Make sense of other students’ explanations  Ask questions of the teacher or other students when they do not understand  Use correct mathematical vocabulary, language, and symbols in their explanation  Share their solutions and thinking with the whole class 53

54. Pilots Available 8 th and 9 th grade “skills” classes to support core classes One teacher per participating school  Use screener to identify and select desired unit  Facilitator guide and student materials for one class will be provided at no cost Results will be analyzed based on student achievement and teacher feedback Contact Kris O’Clair, Mathematics Intervention Coordinator, to be part of pilot this fall. 54

55. Thank you! We know your time is valuable—especially at the start of a school year. Hopefully, this was enlightening as to plans in DPS for the 2009-2010 school year to provide support for our teachers and students in accessing the critical skills in mathematics. For further information, please contact DPS Intervention Coordinator in Teaching and Learning, Mathematics/Science: Dr. Kris O’Clair. 55